Final answer:
To solve the differential equation using the method of undetermined coefficients, assume the particular solution has the form y = Ax + B. Equate coefficients to find the values of A and B. The particular solution is y = x.
Step-by-step explanation:
To solve the given differential equation using the method of undetermined coefficients, we assume that the particular solution has the form y = Ax + B, where A and B are constants. Substituting this into the differential equation, we get 2A + 4(Ax + B) = 4x. Equating coefficients of like powers of x, we find that A = 0 and B = 1. Therefore, the particular solution is y = x.